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Social Indeterminacy

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  • Gil Kalai

Abstract

An extension of Condorcet's paradox by McGarvey (1953) asserts that for every asymmetric relation R on a finite set of candidates there is a strict-preferences voter profile that has the relation R as its strict simple majority relation. We prove that McGarvey's theorem can be extended to arbitrary neutral monotone social welfare functions that can be described by a strong simple game G if the voting power of each individual, measured by the Shapley-Shubik power index, is sufficiently small. Copyright The Econometric Society 2004.

Suggested Citation

  • Gil Kalai, 2004. "Social Indeterminacy," Econometrica, Econometric Society, vol. 72(5), pages 1565-1581, September.
    • Handle: RePEc:ecm:emetrp:v:72:y:2004:i:5:p:1565-1581
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00543.x
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    Cited by:

    1. Beigman, Eyal, 2010. "Simple games with many effective voters," Games and Economic Behavior, Elsevier, vol. 68(1), pages 15-22, January.
    2. Gil Kalai & Elchanan Mossel, 2015. "Sharp Thresholds for Monotone Non-Boolean Functions and Social Choice Theory," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 915-925, October.
    3. Olle Haggstrom & Gil Kalai & Elchanan Mossel, 2004. "A Law of Large Numbers for Weighted Majority," Discussion Paper Series dp363, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    4. Joe Neeman, 2014. "A law of large numbers for weighted plurality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 99-109, January.
    5. Emilio De Santis & Fabio Spizzichino, 2023. "Construction of voting situations concordant with ranking patterns," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 129-156, June.

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